In general, this clustering takes place in an extremely large dimensional space, with as many dimensions as many input data points.
In this particular setup however, we never have more than a few tens of instances to be clustered thanks to the progressive proposal strategy adapted from [1]}.
This means that the clustering is done on a few high-dimensional vectors that is very efficient with most of the clustering algorithms.
Even if there are millions of points in the scene, a single model instance rarely has an extreme number of inliers and, thus, the indices of the non-zero elements in \(v\)  can be stored, making the distance calculation more efficient.
In extreme cases, the min hash algorithm [2]} can approximately find the inlier overlap in constant time.
